Is there a way to set the radius of the new circle select tool by python script
What you are trying to do is change the current context. Instead, you should just be overriding the context.

First step for that would be finding the context that you want to use, that would be our VIEW3D REGION for this case, so we can just cycle through all the context screens available till we find VIEW_3D

for area in bpy.context.screen.areas:
    if area.type == "VIEW_3D":
        #Do stuff


Now just the area itself is not enough as there are different regions inside an area. For our use case we will be needing the window region.

for region in area.regions:
            if region.type == "WINDOW":
                #Do stuff


Now we the required components to define a new context.
What we can do is clone our current context and replace its area and region with the ones we just found.

for area in bpy.context.screen.areas:        #Cycle through all the avaliable areas
    if area.type == "VIEW_3D":               #if area is called VIEW_3D
        for region in area.regions:          #Cycle through all the regions in that area
            if region.type == "WINDOW":      #if the region is WINDOW
                view3dArea = area            #save the area and region in variables
                view3dRegion = region
                break                        #exit the loops

override = bpy.context.copy()                #Make a copy of current context
override['area'] = view3dArea                #Change area to the one we just found
override['region'] = view3dRegion            #Same with the region


Now that we have the right context we just need to pass it into the function.
Simply done by passing it as the first argument as its positional argument.

bpy.ops.view3d.select_circle(override, Other stuff)


You can make a simple function out of this so you can call it whenever you want.

import bpy
def select(x,y,rad):
    for area in bpy.context.screen.areas:
    if area.type == "VIEW_3D":
        for region in area.regions:
            if region.type == "WINDOW":
                view3dArea = area
                view3dRegion = region
                break
    override = bpy.context.copy()
    override['area'] = view3dArea
    override['region'] = view3dRegion
    bpy.ops.view3d.select_circle(override,x=x, y=x, radius=rad, mode='SET')


Simply call that function with the desired radius and coordinates. 

select (300,200,50)




Or you can change the radius and get a bigger selection

select (300,200,100)